This paper considers random walks on a finite group $G$, in which the probability of going from $x$ to $yx, x, y \in G$, depends only on $y$. The main results concern the distribution of the number of steps it takes to reach a particular element of $G$ if one starts with the uniform distribution on $G$. These results answer some random sorting questions. They are attained by applications of group representation theory.
Publié le : 1985-02-14
Classification:
Random walks on a finite group,
limit laws,
group representations,
irreducible characters of $S_n$,
60B15,
60J15,
20C15,
20C20
@article{1176993073,
author = {Flatto, L. and Odlyzko, A. M. and Wales, D. B.},
title = {Random Shuffles and Group Representations},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 154-178},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993073}
}
Flatto, L.; Odlyzko, A. M.; Wales, D. B. Random Shuffles and Group Representations. Ann. Probab., Tome 13 (1985) no. 4, pp. 154-178. http://gdmltest.u-ga.fr/item/1176993073/